Improving semi-groups bounds with resolvent estimates

Amélioration des bornes sur les semi-groupes par des estimations de la résolvante

Bernard Helffer (1) , J Sjöstrand

1 LMJL - Laboratoire de Mathématiques Jean Leray

The purpose of this paper is to revisit the proof of the Gearhardt-Prüss-Hwang-Greiner theorem for a semigroup S(t), following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on S(t) in terms of bounds on the resolvent of the generator. A first version of this paper was presented by the two authors in ArXiv (2010) together with applications in semi-classical analysis and a part of these results has been published later in two books written by the authors. Our aim is to present new improvements, partially motivated by a paper of D. Wei. On the way we discuss optimization problems confirming the optimality of our results.

Domaines: Mathématiques [math]

Bernard Helffer, J Sjöstrand. Improving semi-groups bounds with resolvent estimates. 2021. ⟨hal-03175983⟩